Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-6y &= 9 \\ -2x-7y &= 7\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-7y = 2x+7$ Divide both sides by $-7$ to isolate $y$ $y = {-\dfrac{2}{7}x - 1}$ Substitute this expression for $y$ in the first equation. $-3x-6({-\dfrac{2}{7}x - 1}) = 9$ $-3x + \dfrac{12}{7}x + 6 = 9$ Simplify by combining terms, then solve for $x$ $-\dfrac{9}{7}x + 6 = 9$ $-\dfrac{9}{7}x = 3$ $x = -\dfrac{7}{3}$ Substitute $-\dfrac{7}{3}$ for $x$ back into the top equation. $-3( -\dfrac{7}{3})-6y = 9$ $7-6y = 9$ $-6y = 2$ $y = -\dfrac{1}{3}$ The solution is $\enspace x = -\dfrac{7}{3}, \enspace y = -\dfrac{1}{3}$.